Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C47×H(7,𝔽2) ⋊ C2 |
| Sylow | C47 ⋊ #60401 |
4854 conjugacy classes of subgroups; only the 807 normal subgroups are shown.
This group has 4854 conjugacy classes of subgroups — too many to draw. Only its 807 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1504 |
A minimal faithful permutation representation — 5 generators on 79 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(52,63)(56,69)(59,73)(61,74)(65,76)(67,77)(71,79)(75,78);(48,52)(49,56)(50,59)(51,61)(53,63)(54,65)(55,67)(57,69)(58,71)(60,73)(62,74)(64,75)(66,76)(68,77)(70,78)(72,79);(48,51)(49,55)(50,58)(52,61)(53,62)(54,64)(56,67)(57,68)(59,71)(60,72)(63,74)(65,75)(66,70)(69,77)(73,79)(76,78);(48,50)(49,54)(51,58)(52,59)(53,60)(55,64)(56,65)(57,66)(61,71)(62,72)(63,73)(67,75)(68,70)(69,76)(74,79)(77,78);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49,53,57)(50,54,60,66)(51,55,62,68)(52,56,63,69)(58,70,72,64)(59,65,73,76)(61,67,74,77)(71,78,79,75)Polycyclic presentation:
2^8,47|a^2=h,b^a=bf,c^a=cg,i^a=i^46,g^b=gh,f^c=fh,e^d=eh1553 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1036331);